Calculating residue in the \((k+1)\) -th order pole at \(\varepsilon = i(\Gamma + i \gamma _s)\) , one can express the integral (REF ) in terms of the ortho-normalized set of the Laguerre functions (the products of the Laguerre polynomials and exponential factors)
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\(a_s^{(k)}(t) = \exp (- 2k\pi \Gamma t) \exp (-(\gamma _s (t - 2k\pi )))\, ,\) 
